English

The Double Complex of a Blow-up

Algebraic Geometry 2019-07-30 v2 Complex Variables Differential Geometry

Abstract

We compute the double complex of smooth complex-valued differential forms on projective bundles over and blow-ups of compact complex manifolds up to a suitable notion of quasi-isomorphism. This simultaneously yields formulas for 'all' cohomologies naturally associated with this complex (in particular, de-Rham, Dolbeault, Bott-Chern and Aeppli).

Keywords

Cite

@article{arxiv.1808.02882,
  title  = {The Double Complex of a Blow-up},
  author = {Jonas Stelzig},
  journal= {arXiv preprint arXiv:1808.02882},
  year   = {2019}
}

Comments

Inlcuded an example and discussions of product structures and extensions to singular spaces. Minor improvements throughout. Mainly following referee suggestions

R2 v1 2026-06-23T03:28:10.905Z